5.22 In order to test the effectiveness of a sales training program proposed by a firm of training specialists, a home furnishings company selects six sales representatives at random to take the course. The data are gross sales by these representatives before and after the course.

Representative Sales Before Sales After 1 90 97 2 83 80 3 105 110 4 97 93 5 110 123 6 78 84

(a) State the null and alternative hypotheses and use the sign test to find a P value relevant to the question of whether the course is effective.

(b) Use the sign-test procedure at level nearest 0.90 to find a two-sided confidence-interval estimate of the median difference in sales (after–
before). Give the exact level.

(c) Use the signed-rank test to do (a). What assumptions must you make?

(d) Use the signed-rank test procedure to do (b).